Introduction to Global Navigation Satellite Systems
Introduction to Global Navigation Satellite Systems ASEN 5090
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INDOOR GNSS ASEN 5090 Lecture 38 Wth Information from B Eissfeller presented at First International Summer School on GNSS Berchtesgaden Germany Sept 2007 And examples from navsynccom Colorado Umvars vat may it may ASEN 5090 LECTURE NOTES 7 LARSON AXELRAD MOTIVATION E911 Finding people in distress indoors FCC E911 mandate Monitoring of elderly children people with disabilities Firefighters emergency personnel soldiers Tourism E oom merce Colorado Unix25391an may i may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 2 Conventional GPS operations Received signal power is 157 dBW SNRs are 1020 Acquisition is performed by a search over delay and doppler Receiver transitions from acquisition to tracking Channels are designed primarily for tracking can track signals at a much lower power level than acquisition Multipath is bad because it degrades accuracy Colorado Unix25391an may it may ASEN awn Lacrqu NOTES 7 mason AXELEAD a Indoor GPS operations No distinction between acquisition and tracking Channels are designed primarily for rapid acquisition Aiding from an antenna with clear view of the sky somewhere nearby used to provide info usually available from acquisition or navigation filter Multipath is good because it increases SNR Satellite ephemeris clock and NAV bits provided by an auxiliary link Time tag provided by external link Frequency of rx clock provided by external link Approximate position known Massively parallel correlators Long coherent integration Very long noncoherent integration Colorado Univus ya may it may ASEN awn Lacrqu NOTES 7 mason AXEUEAI 4 HISTORY OF INDOOR GPS from Eisfeller Colorado Univus ya may it may 1981 Aiding of acquisition by Doppler and ephemeris Taylor amp Sennot US Patent 44451 18 1991 Transmission of pseudoranges from mobile system to central facility and remote positioning TIDGET NAVSYS 1997 Peterson IONGPS 1997 Measuring GPS Signals Indoors 1998 Snaptrack used 1 sec of data to acquire and measure FFT based 2000 Chansarkar and Garin ION NTM 2000 2001 GlobalLocate Indoor chip with 16000 correlators 2001 Snaptrack Qualcomm GPSOneTM Chip Assisted GPS 2004 SiRFStarlll W High sensitivity chip with 200000 correlators ASEN awn Lacrqu NOTES 7 mason AXEUEAI a SIGNAL LEVELS and ATTENUATION Outdoor 126 to 130 dBm Indoor House 130 to 145 dBm Inside mostly gIass office building 435 to 160 dBm Inside underground parking 150 and lower Indoor signals are 2030 dB weaker than outdoor Sensitivity of receiver has to be improved by this amount Colorado Unix25391an may it may ASEN awn Lacrqu NOTES 7 mason AXEUEAI a APPROACHES Extend the coherent integration time to maximum possible value a Requires external aiding to reduce frequency errors a To keep loss to less than 1 dB freq error must be less than 14Tco u V peoff navigation data bits Use noncoherent integration to further accumulate signal power over m coherent integartions in Signal to noise ratio is proportional to sqrtm Colorado Unix25391an may it may ASEN awn Lacrqu NOTES 7 wasoN AXELEAD 7 PARTHUS Outside antenna used for master channel sets doppler time gets data bits Inside antenna tracked with slave channel Doppler caused by user motion and multipath Coherent integration for 256 ms Gives 120 dB proc gain Noncoherent integration for 1 sec Colorado Unix25391an may it may ASEN awn Lacrqu NOTES 7 wasoN AXELEAD a FFT ACQUISITION Take a block of sampled data si of at least 1 ms Compute complex FFT of samples X Generate a local replica of the code with carrier replicas spaced at 1kHz intervals Compute complex FFT of local replicas L Multiply conjX x L this is R Compute inverse FFT and find maximum value This bin gives the delay n and frequ of the signal to resolution of 1 sample and 1 frequ bin 1kHz Colorado Unix25391an may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI a From googling found a nice description at navsynccom Indoor use 173 dBW acquisition and 185 dBW tracking Size 6 by 5 by 1 cm Plugs into a laptop USB Colorado WWW may it may ASEN awn LECTUPE NOTES 7 LAQSONAXELRAD m Acquiring and tracking Colorado Univus ya may it way First you need to do a twodimensional search of the phase of the desired satellite signal and the carrier frequency plus Doppler of the satellite Phase search is performed by shifting the phase of the replica PRN code generated by the receiver until it correlates with the received satellite PRN code The carrier frequency search is performed by adjusting the rate of the PRN code generator on the receiver until it correlates with the received satellite carrier frequency plus Doppler A full sky search can take significanttime to perform which directly affects the Time to First Fix TTFF as well as the sensitivity of the receiver ASEN awn rarqu NOTESV LAksoN AXEUEAI u How to overcome I In one example I found online rapid TTFF was achieved by massively increasing the number of correlators applied to each receiver channel with a maximum number of 12288 correlators This receiver was tested in various real life scenarios with the following locations to demonstrate the ability of the CW25 receiver to track satellites in areas of poor signal strength Colorado Univus ya may i may ASEN awn LECTUPE NOTES 7 LARSONAXELPAD 12 6 sats 157 182 dBW 17 m positions Colorado unmnynq mom 4 may ASEN 5090 LECTURE NOTES 7 LARSON AXELRAD 13 4 sats 171 182 dBW 27 m positions Colorado Huh35Kan tarmac H mm ASEN 5090 LECTURE NOTES 7 LARSON AXELRAD 14 9 sats 160 187 dBW 17 m positioning Colorado mimnyni carom n Ewidu ASEN 5090 LECTURE NOTES 7 LARSON AXELRAD 15 References on Indoor and Weak signal acquisitiontracking Watson et al Investigating GPS Signals Indoors with Extreme HighSensitivity Detection Techniques Navigation Vol 52 No 4 p 199213 Haddrell T and AR Pratt Understanding the Indoor GPS Signal ION GPS 2001 p 14871499 Psiaki ML Block Acquisition of Weak GPS Signals in a Software Receiver ION GPS 2001 p 28382850 Colorado Unix25391an may it may ASEN awn LECTUPE NOTES 7 LAkSONAXELkAb m Published in 2001 GPS World This cellphone market opportunity represents one of the primary drivers behind the search for a GPS receiver technology that goes beyond a singlechip solution to what could be called a quotnochipquot solution Such a solution would share functionality with elements of the wireless communications handset itself Successful adoption of GPS into cell phones requires that the technology meet new demands including indoor operation nearinstantaneous time to first fix and very low power consumption Feedback from phone manufacturers suggests that incorporating GPS should add no more than 10 to the parts cost of a wireless handset Colorado Univus ya may i may ASEN awn LECTUPE NOTES 7 LARSONAXEUEAI l7 Other news Nokia to launch indoor GPS service in coming months 2008 Using WLAN wireless LAN networks Nokia hopes to give the power of location to people within buildings where users could employ their mobile phones to locate the office printer a free meeting room or even their child in a busy shopping centre lphone But the AGPS Assisted GPS solution on iPhone 36 goes a step further using a unique approach to find the closest satellites and more quickly identify your position That gives you a faster fix on your location than with regular GPS How do you thinkthey do this Geotags all photos Colorado Univus yal may it may ASEN awn LECTUPE NOTES 7 arson gums IE LINK BUDGET ASEN 5090 Lecture 30 WITH FIGURES FROM TEXTBOOK MISRA amp ENGE Colorado Unmnm my a may ASEN 5090 LECTURENOTESV LARSONAXELRAD OUTLINE amp KEYWORDS Path Loss Flux Density Antenna Gain EIRP Noise CNo SNR Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 2 FLUX DENSITY Flux density is powersurface area Flux PT 4 RZ warmmZ Flude ng 101og1n 41 20101n R dBWmz Power spatial densm V PT 2 PT wan A 4393 V we m2 Misra amp Enge Figure 1011 Colorado Unix25391an may i may ASEN awn LECTUEE NOTES 7 wasom AXEUEAI a FREE SPACE LOSS Space loss is spreading of signal due to enlarging sphere Z LS E A Ls 20101n g 20101n 41R 20101n A Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 4 GPS SATELLITE GEOMETRY RE 6371 km cl RSV 26560 km I I 1 RE sinel 900 Nadlrangle 06 sm R SV Eanh Misra amp Enge Figure 1011 Univershyo Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 5 GPS TRANSMISSION GPS Satellites transmits 27W 143 dBW on CA L1 Can be 24 dB higher Antenna beamwidth is 213 deg Earth subtends 139 deg as seen from GPS satellite Antenna focuses more gain towards the limb of the earth to compensate for additional path loss and create constant received power on earth surface Colorado Unix25391an may it may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI a GPS ANTEN NA PATI39ERN GPS Elements transmit overfrequency range of 12001600 MHz Ideal Beamwidth is 28 deg with 21dB dimple in the middle Antenna gain pattens described in previous lecture Colorado Unix25391an may it may ASEN awn LECTUle NOTES 7 wasoN AXEUEAI 7 EIRP Effective isotropic radiated power EIRP EIRPJiB PM GTdB Nadir angle 0 90 deg cc 40 deg cc 5 deg Elevation 9 90 deg 9 40 deg 9 5 deg angle GT 102 dB 129 dB 121 dB EIRP 245 dBW 272 dBW 264 dBW Colorado Unix25391an may i may ASEN awn LECTUEE NOTES 7 wasom AXEUEAI a gtZmZZgt 922 w muum0ltm gtmmgt aka A n m 3 n3 015 COQOEQO is 5 52 53 SE SE EEK 23mm immoz 59 a GPS POWER RECEIVED BY ISOTROPIC ANTENNA on EARTH 155 E 156 E a 157 g Q 158 8 2 159 CD 8 160 cc 161 0 1O 20 30 40 5O 60 7O 80 90 Elevation angle degrees Misra amp Enge Figure 1011 Colorado Universny of Colorado at Bouider ASEN 5090 LECTURE NOTES LARSON AXELRAD 10 RECEIVED POWER DENSITY Received power density dB is EIRP space oss atmospheric oss P TdB PDdB G SLdB AL 715 Elevation angle 990 deg 9 40 deg 9 5 deg PD 1346 dBWm2 1326 dBWm2 1346 dBWm2 Colorado Unix25391an may it may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI RECEIVING ANTENNA CPRPDARE PTGTARE PTGTGRAZ 4r PTGTGR A 2 LA 41RZ LA 41RZ LA 41R C45 PM Gm GRdB LAdb SL415 Elevation angle 9 90 deg 9 40 deg 9 5 deg GR patch 4 dBic 2 dBic 4 dBic antenna PR 156 dBW 156 dBW 164 dBW Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 12 NOISE Thermal noise in the receiver noise figure Natural noise outside ambient Reflected signals other GNSS signals other transmissions Noise power is noise spectral density times bandwidth PN NUBW Noise spectral density is 201 to 203 dBWHz Noise Temperature is between 290 to 320 K PN kquBW k 138x1023JK Boltzmann39s constant qu equivalent temperature NU kqu Colorado Unix25391an may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 13 NOISE FIGU RE Noise figure of a device CNn W CNu m T FTu17 so TE FTu 1Tu F Friis formula for cascaded devices T TR TEV1 5392 Q 6le Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 14 NOISE IN A GPS RECEIVER Sun WM TA 100 K T T E2 E3 TR 2 I G1 G162 Grourld Cable and Cable and radiation filter filter G1 08 G3 01 gt F1Z1dB F31OdB T512754 K TE32610 K Misra amp Enge Figure 1011 Colorado Universny of Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 15 CNo SNR Ratio of signal to noise spectral density typically 35 to 48 dBHz C N n Signal to noise ratio depends on the bandwidth that you are working with N Colorado Univus ya may it may ASEN awn LECTUkE NOTES 7 wasoN AXEUEAI m Fourier Series and Transforms ASEN 5090 Lecture 26 Colorado aaaaaaaaaaaaaaaaaaaaaaaa g ASEN 5090 LECTURENOTESV LARSONAXELRAD OUTLINE Review Fourier Series for Periodic Pulse Fourier Transform for single Pulse Parseval s Theorem Modulation Filters Read Book On 8 Colorado Unix25391an may i may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 2 Periodic Functions A periodic function of period Tp 1fp fl nTp ft Can be expressed by a Fourier Trigonometric Series as ft a0 2 an cosn2rrfpt b sinn2rrfpt oo 1 Colorado Unix25391an may i may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI a Fourier series for a signal that is periodic in P m ft a0 2 an cosn2rrfpt b sinn2rrfpt 0 S D Colorado Unix25391an may i Wm n 1 ff w PZ i f ftcosn2rrfpt dt PZ P 2 i f ftsinn2rrfptdt 2 7P ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 4 Change of variable Let x anpt sofortTpx2rr The function f is then expressed as fx a0 2 cosmcbn sinmc quot1 Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI a Fourier Coefficients 1 1n g fxcosmcdx 1I g fxs1nmcdx Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI a Examples a0 an bn 1 1 1 ConstantA EiAdxA giAcosnxdx0 fxsmnxdx0 1 quot 1quot 2 1quot cosnx ifcosnxdx0 ifcos nxdx1 ifcosnxsmnxdx0 257 in in 1 1 1 cosmx mtn E cosmxdx0 cosmxcosnxdx0 cosmslnmdx0 sinnx ifsinmcobc0 ifsinmcosmcolx0 ifsinznxdxl 2 in in Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 7 Square Wave A 271 471 x 1 0 1 ag f Adx Adx0 A 1f3975ltxlt0 7 x 0 A if0ltxltn U 71 an if AcosmcdxLfAcosmcdx0foralln 7L 750 1 0 1 2A 1 7 A39 dxi A 39 dx71 J Slnmc Slnmc GOSH bl 1720 I23 b40elc n 371 so fx 4A sinx sin3xsin5x n Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI a Periodic rectangular pulse f A 01fMgtg 7 T2 T2 PNT mA KM NH 1 pr PZ TZ AT A 20 fzdz Adzii 2 L P N Z P T AsinnanlT an iz zflcosn2nfpldz 7 2Acosn2njzldlW TZ u a2AsinmfFT 2AsinmN 2A In quot nn N mN N N Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI a Fourier representation of a periodic rectangular pulse A 2A mt ft 7n1smcwcosnerr o x ElA 5 Sedes for m 39 lT1 023 66 5 n V V and fp1 e3 2 5 72 15 t o 5 u u 5 t 15 2 2 5 x Eli Zoomed in to Show lines new aw m iqu NOTES 7 wasoN AXEUEAI m FOURIER TRANSFORM For any xt you can take a Fourier Transform to produces a continuous function off Fx Xf ixo e39fm dt Fourier Transform of unit pulse FptPf fpre quot dt 12 sin erft f cosZJrftdt dt sinc2rrf erf 712 UColorado quotmm may i may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI u Fourier Transform of a Pulse 0 ifxgt1 4A7 1ifxlt1 fx fx Aw cos wx Bwsin am 100 Awfvcoswv dv Bw fvcoswv dv 1 Aw cos aw dv 7 71 1 s1n aw Zsm a 2 s1ncw 7m 1 7m 7139 UColorado quotmm my a may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 12 Sinc and Sinc2 Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 13 Nulls in Fourier Series or Transform of PulsePulse Train 2A N sinnrrN mrN an n null occurs for F any 1nteger value P f sine er f null occurs for 2f any integer value Colorado Hun25391an my may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI r4 PARS EVAL S THEOREM P UColorado quotmuslian my al may 1 t0 T0 1 t0 T0 00 f x2 Idt f 2 xne mf xldt t0 0 t0 n 1 00 0T0 j27mf0t szn J xle dt 0 n oo oo oo 2 Swen2 xn quot40 quot40 Signal power IS sum of sqg of all exponential baSIS amplitudes ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI IE MODULATED SIGNALS Modulation is a nonlinear process st xtcos2nf0t What is the spectrum of st FS xtcos Znfooevzn dt xte21rfn erJZJrfnt ejzn dt j xte21rf fu xte121rffnz dt XffoXffo ASEN awn LECTUEE NOTES 7 wasoN AXEUEAI m FILTERS Bandwidth BVV Nulltonull 3dB Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 17 Orbits C0 or Unmnm my a may ASEN 5090 LECTURENOTESV LARSONAXELRAD Outline Kepler s Laws 2 body motion Orbital Elements Position and Velocity Orbital Perturbations GPS Satellite Orbit Determination GPS Broadcast Ephemeris Colorado ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 2 Kepler39s Laws pmer dimmm Describe motion of an object under a central force Planets take the path of an ellipse with the Sun at the foci The linejoining the planet to the sun sweeps out equal areas in equal times The square of the orbital period is proportional to the cube of its mean istan e to the sun Cn rarfn ASEN awn Lacrqu NOTES emsoN Mam 3 Orientation of the orbit plane nunma poullull nv mm 39Y Colorad0 wnm mmnux Unmnm my may ASEN awn LECTUPE NOTES iLuzsoN AxmAb 4 Keplerian Orbital Elements Size and shape of the orbit a semimajor axis of the ellipse e eccentricity ofthe ellipse b axll ez Orientation of the orbit 52 right ascension of the ascending node i inclination to argument of perigee Position within the orbit pick one 1 true anomaly u argument of latitude w v E eccentric anomaly Folorari g mean anomaly ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 5 Kepler s Equation M E esinE M EMU nt t a 2 P 2n 7 Kepler39s 3rd law u 271 u n 7 7 mean motlon P a apogee a gt geocenter perigee Colorado ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI s Position within the orbit plane Solve Kepler s equation for E iteratively I Then compute the true anomaly Il eZ sinE smv l ecosE osE e cosv l ecosE 1 V1 ez sinE v tan cosE e 11 82 And the distance from the focus 1 E r a ecos 1ecosv ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 7 Colorado Newton s laws and two body motion Newton showed why Kepler s empirical laws were true z For motion under a central force 1 L 0 r E Fxx Angular momentum is constant 11 pm 1 ez Energy is conserved V2 M3l Colorado ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI s Orbital Perturbations central force is 05 ms2gt Source Acceleration Perturbation Type ms2 3 hrs Earth oblateness 5 x10395 2 km 3 hrs secular 6 hr J2 Sun amp moon 5 x10396 5150 m 3 hrs secular 12hr Higher Harmonics 3 x10397 580 m 3 hrs Various Solar radiation 1 x 10397 100800 m 2 days Secular 3 hr pressure Ocean amp earth 1 x10399 0 2m 2 days secular 12hr tides Earth albedo 1 x10399 115m 2 days pressure Colorado ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI GPS Satellite Orbit Determination Control segment collects range measurements at monitoring stations Uses precise orbit determination software including high fidelity models of perturbations to estimate position and velocity and clocks and many other parameters of the satellites Representation of the orbit in the broadcast message is a quasi Keplerian parameterization that fits best over a 2 hour segment a toe time of ephemeris IODE issue of data ephemeris u Keplerian elements a 2 drift rates amp An in 6 coefficients for harmonic corrections Colorado ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI m Broadcast Ephemeris see website mh 11 rf r uvlinw mm Mu m Wm nu Firm m n n a m n arr llr m lt m mm 14m I 1nmmmv 1 a 1 Colorado ASEN awn LECTUPE NOTES 7 LARSON AXEUEAI m mumn m mumps n 7 mm sun In rally mr u w mamquot m xg it 42 w u or 76 2 mmz 5 r mama mung I u 7 w mm full pawn 7 1 m muTv r Colorado was cps lmkimmlpumlw om LI39N wank 39mallnn m 7 E a E w m W mmn mum m mm mwm Ur mum mguumm ur mum quut mm mm mum my 1 mum l mum mum w gun an r mum mum w 1mm mum w iwlma r pymmm m arm H mm mm m lmghmlv r um um E w mmlumm ASEN awn LECTUkE NOTES 7 wasom AXELRAD 12 cus OmegaO omega Omegadot ldOt accuracy health zeros 1 noeph Foloradgx ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 13 When you code this up I will give you code that reads the broadcast ephemeris You should have a function that computes the location XYZ of a satellite at a given time lnput is broadcast ephemeris elements and PRN number The broadcast elements could also be defined as a global You will have a separate function that computes what you really want to know which isthe geometric range for a satellite that transmitted the signal at Tt and a receiverthat received it at Tr Colorado ASEN awn Lacrqu NOTES 7 wasoN AXEUEM 14 RECEIVER OVERVIEW WITH FIGURES FROM TEXTBOOK MISRA amp ENGE UColorado quotmm my I may ASEN 5090 LECTURENOTESV LARSONAXELRAD Receiver Elements Antenna Frequency Synthesizer generate reference clock Front End Amplify filter downconvert signal AD Conversion Sample signal usually 1 or 2 bits Signal Processing Channels Extract 1 fD 66 amp data bits Navigation Processor Solve for position Figures are from Misra and Enge 1St Edition Colorado Univus ya may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 2 Antenna 0 Burnout protection Bandpass filter Lownoise amplifier 39 Satellite 1 Analog to digital 33 Acquisition converter ADC Tracking 0 Data demod Applicationspecific processing Amplifiers 0 Down converters Bandpass filters Estimation of Position Velocity Time l I I I I I I I I I A i Software radio techniques strive to minimize the analog signal conditioning 4 Displays and data storage Figure 91 GPS receiver block diagram Colorado Unmemmiof Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD Antenna frequency BPF Reference Burnout protection Bandpass filter 0 Lownoise amplifier frequency BPFs 39 ignaii onditiortir c7322 Code and carrier measurements to PVT estimator Mixer and intermediate Local oscillator Frequency oscillator quot synthesizer Bandpass 1572 Dopplerr a sampling r removal Local oscillator 2 l kg DLL amp PLL filters Figure 93 Expanded block diagram for the signal processing portions of the receiver empha sized in this chapter Colorado Uniuersittrof Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 4 Colorado 0 5mm W Ira1 fur gt tj quot LD quotltr2096quotr Icos27tfz1 5quotts4 19 imwme i cos22tlt 2fr Lownoise mpiifier LNA a Band pass fiiter centered on f 1 RF BPF i r x i 7 Figure 94 Mixers and intermediate frequency stages University of Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 5 BPF Amplifier BPF LNA 20 dB so MHz gt 40 dB gt so MHz X quotl V L BPF Amplifier BPF BPF 3MHz 40dB 3MHz r X gt 2MHz V coslznifpwzwel Figure 95 Multiple mixers and intermediate frequency stages are often employed Colorado University3f Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 6 3azcos 22 A f f0 Af f0 93 I I I U 2121 17F le Figure 96 Fourier transforms before and after down conversion Colorado Unimarsity of Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 7 A Continuous analog signal A 1 L lt Four level amplitude Discrete time signal I l l l I I giifaf39S u i39eVe39 iii iiIiiiiiiIiiiiiiiiiiiii 98 Types of signal continuous analog amplitude quantized discrete time and digital quotQ pr V39H Colorado University of Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 8 Analog to Digital Conversion Sampling frequency must be higherthan Nyquist what is required for CA For PY 1 bit AD converters often used in low cost GPS in Why does this worK in Some loss of signal but not much 2 bit requires use of Automatic Gain Control AGO to keep samples welldistributed Higher resolution not very useful Colorado Univus ya may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI a WWW AMAHANNA hv A Am VVV V Figure 913 Bandpass sampling of a desired signal and an alias Colorado University of Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 10 ALIASING Signals at frequencies above the Nyquist are aliased orfolded into the range of 0 to Nyquist Low pass filtering priorto sampling is required to avoid this Colorado Unix25391an may i may ASEN awn LECTUPE NOTES 7 LARSON AXEUEAI u FRONT END Antenna 5i Samples of all satellites and in band noise LO local oscillator Colorado Umvars va may it may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 12 RECEIVED SIGNAL MODEL for ONE SATELLITE st JEDt Txt TCOS27 le fD t9 after downconversion sIF t JEDt Txt TCOS27 fD t9 ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 13 DOPPLER REMOVAL amp CORRELATION PROCESSING Integrate and dump cos2rrfIF2Dl 201 1 What does the output look like if the estimates of delay doppler and phase are perfect UColorado quotwastian may at may ASEN awn LECTUkE NOTES 7 wasoN AXEUEAI 14 IN PHASE and QUADRATURE PROCESSING Integrate and dump aaaaaaaaaaaaaaaaaaaaaaaa g ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 15 CORRELATOR OUTPUT SIF zJEDz 1xz 1cos271 FfDz0 reference signals cos2nfIFfD cos2n FfD a er doppler removal we have JEDl 1xl 1cos2nAfDl A01JEDz 1xz 1sin2nAfDl A0 a er correlation Tint Q I xz 1 cz fcos2nAsz A0dz Int 0 Tint JED f xl 1 gt90 fsin 271Asz A0 dz mt 0 5033611 SQ fm j UColorado quotmm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI m AMBIGUITY FUNCTION To get rid of effecf of DATA and Phase errors take magnitude ISZI I Sflkfls l H717 Ambigu y funC On xiS the fbortelatdrOutput as a function 1 f39 DOD P39GF anddelay je rrdrs w 08 1 1 Universityof Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 17 194 UNDERSTANDING GPS PRINCIPLES AND APPLICATIONS SEARCH Signal location versus 8 E 1 cell 1 2 Chip search threshoI d 4 1Doppler bin I 6 4 2 Start of search expected value of 39 1 direction Doppler 3 5 7 Doppler lt 1023 chips t search sequence 39 a m Figure 534 Two dimensional CIAcode search pattern K u i Coloram University of Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 18 DETECTION Section 113 How do we specify if a signal is acquired or detected in a particular cell Set threshold based on probability of detection and probability of false detection Probabilities depend on the signal to noise ratio which in turn depends on CNO and integration time V th typical signal levels you are very likely to make an error on a single 1ms measurement Colorado Univus ya may it may ASEN awn Lacrqu NOTES 7 mksoN AXEUEAI w TYPES OF ACQUISITION Warm Start in Have navigation data i Know which satellites should be in view and expected doppler a Can you assume you knowthe delay I Cold Start i Know nothing i What is the best way to search What makes a receiver most effective for acquisition Reacquisition aided acquisition or hot start i Know delay doppler and data Colorado Umvus ya my r may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 2n Colorado Unmnm my a may ASEN awn LECTUkE NOTES 7 wasth AXEUEAI 2 Colorado Unmnm my a may ASEN awn LECTUPE NOTES imwsoN AXEUEAI 22 Colorado Unmnm my a may ASEN awn LECTUPE NOTES imwsoN AXEUEAI 23